A066491 Twin prime gaps: Pairs k, k+1 such that f(k) = f(k+1), where f is the prime gaps function given by f(m) = prime(m+1)-prime(m) and prime(m) denotes the m-th prime.

2, 3, 15, 16, 36, 37, 39, 40, 46, 47, 54, 55, 55, 56, 73, 74, 102, 103, 107, 108, 110, 111, 118, 119, 129, 130, 160, 161, 164, 165, 184, 185, 187, 188, 194, 195, 199, 200, 218, 219, 239, 240, 271, 272, 272, 273, 291, 292, 339, 340, 358, 359, 387, 388, 419, 420

Offset

1,1

Comments

Each pair of terms yields a triple of primes in arithmetic progression; e.g., 2,3 yields the prime triple 3,5,7.

Links

Table of n, a(n) for n=1..56.

Formula

a(2*n-1) = A064113(n); a(2*n) = A064113(n) + 1. - Andrew Howroyd, Oct 22 2023

Example

2,3 is a twin prime gap since f(2) = f(3) = 2. 54,55 is a twin prime gap since f(54) = f(55) = 6.

Mathematica

(* to find the smaller number in each twin prime gap *)
f[n_] := Prime[n + 1] - Prime[n]; Select[Range[1, 10^3], f[ # ] == f[ # + 1] &]

Crossrefs

Cf. A001223 (f), A064113.

Sequence in context: A309765 A238691 A241721 * A282383 A299486 A173334

Adjacent sequences: A066488 A066489 A066490 * A066492 A066493 A066494

Keyword

easy,nonn,tabf

Author

Joseph L. Pe, Jan 03 2002

Extensions

More terms from Jason Earls, Jan 05 2002

Status

approved